US8068535B2 - Robust iterative linear system solvers - Google Patents
Robust iterative linear system solvers Download PDFInfo
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- US8068535B2 US8068535B2 US12/058,494 US5849408A US8068535B2 US 8068535 B2 US8068535 B2 US 8068535B2 US 5849408 A US5849408 A US 5849408A US 8068535 B2 US8068535 B2 US 8068535B2
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
- G06F17/10—Complex mathematical operations
- G06F17/11—Complex mathematical operations for solving equations, e.g. nonlinear equations, general mathematical optimization problems
- G06F17/12—Simultaneous equations, e.g. systems of linear equations
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04B—TRANSMISSION
- H04B1/00—Details of transmission systems, not covered by a single one of groups H04B3/00 - H04B13/00; Details of transmission systems not characterised by the medium used for transmission
- H04B1/69—Spread spectrum techniques
- H04B1/707—Spread spectrum techniques using direct sequence modulation
- H04B1/7097—Interference-related aspects
- H04B1/711—Interference-related aspects the interference being multi-path interference
- H04B1/7115—Constructive combining of multi-path signals, i.e. RAKE receivers
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04B—TRANSMISSION
- H04B1/00—Details of transmission systems, not covered by a single one of groups H04B3/00 - H04B13/00; Details of transmission systems not characterised by the medium used for transmission
- H04B1/69—Spread spectrum techniques
- H04B1/707—Spread spectrum techniques using direct sequence modulation
- H04B1/7097—Interference-related aspects
- H04B1/711—Interference-related aspects the interference being multi-path interference
- H04B1/7115—Constructive combining of multi-path signals, i.e. RAKE receivers
- H04B1/712—Weighting of fingers for combining, e.g. amplitude control or phase rotation using an inner loop
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04B—TRANSMISSION
- H04B7/00—Radio transmission systems, i.e. using radiation field
- H04B7/02—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas
- H04B7/04—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas
- H04B7/08—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the receiving station
- H04B7/0837—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the receiving station using pre-detection combining
- H04B7/0842—Weighted combining
- H04B7/0848—Joint weighting
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04B—TRANSMISSION
- H04B2201/00—Indexing scheme relating to details of transmission systems not covered by a single group of H04B3/00 - H04B13/00
- H04B2201/69—Orthogonal indexing scheme relating to spread spectrum techniques in general
- H04B2201/707—Orthogonal indexing scheme relating to spread spectrum techniques in general relating to direct sequence modulation
- H04B2201/70707—Efficiency-related aspects
-
- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04B—TRANSMISSION
- H04B2201/00—Indexing scheme relating to details of transmission systems not covered by a single group of H04B3/00 - H04B13/00
- H04B2201/69—Orthogonal indexing scheme relating to spread spectrum techniques in general
- H04B2201/707—Orthogonal indexing scheme relating to spread spectrum techniques in general relating to direct sequence modulation
- H04B2201/7097—Direct sequence modulation interference
- H04B2201/709727—GRAKE type RAKE receivers
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04B—TRANSMISSION
- H04B7/00—Radio transmission systems, i.e. using radiation field
- H04B7/02—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas
- H04B7/04—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas
- H04B7/08—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the receiving station
- H04B7/0837—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the receiving station using pre-detection combining
- H04B7/0842—Weighted combining
- H04B7/0848—Joint weighting
- H04B7/0854—Joint weighting using error minimizing algorithms, e.g. minimum mean squared error [MMSE], "cross-correlation" or matrix inversion
-
- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04B—TRANSMISSION
- H04B7/00—Radio transmission systems, i.e. using radiation field
- H04B7/02—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas
- H04B7/04—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas
- H04B7/08—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the receiving station
- H04B7/0837—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the receiving station using pre-detection combining
- H04B7/0842—Weighted combining
- H04B7/0848—Joint weighting
- H04B7/0857—Joint weighting using maximum ratio combining techniques, e.g. signal-to- interference ratio [SIR], received signal strenght indication [RSS]
Abstract
Description
Rw=h (1)
arise. Here, R is an N×N matrix that can be an impairment covariance matrix with known values, h is an N×l vector with known values, which are net channel coefficients, and w is an N×l vector that needs to be determined and contains combining weights. Methods like Gaussian elimination, LU decomposition, QR factorization, or other known methods can be employed to solve for the unknown vector w. These methods typically require O(N3) (i.e. “of the order of N3”) operations to determine w, which may be too computationally complex for many applications. Also, the aforementioned methods may encounter numerical problems if the matrix R is ill-conditioned.
w i+1 =w i +g(r i)
r i+1 =f(h−Rw i+1) (2)
Here, ri+1 is the residual error vector at iteration i+1, f(h−Rwi+1) indicates an expression that is a function of the combining weights at iteration i+1 (e.g. f(h−Rwi+1)=h−Rwi+1), and g(ri) indicates an expression that is a function of the ith residual error vector (e.g.
where pi+1=ri+βi+1pi and
Here w0 represents the initial guess at the solution and r0 is the residual error due to the initial guess. Many iterative algorithms fit into the framework of the equations (2), but other formulations are possible.
Ruw=h
or a quantity derived therefrom can be used in a method for stopping the iterations, so that the iterations are stopped when e.g. the successively calculated values of the signal to interference plus noise ratio have a specific, predetermined behaviour.
Claims (12)
Priority Applications (3)
Application Number | Priority Date | Filing Date | Title |
---|---|---|---|
US12/058,494 US8068535B2 (en) | 2008-03-28 | 2008-03-28 | Robust iterative linear system solvers |
EP09726265.3A EP2269318B1 (en) | 2008-03-28 | 2009-02-23 | Robust iterative linear system solvers |
PCT/SE2009/050196 WO2009120133A1 (en) | 2008-03-28 | 2009-02-23 | Robust iterative linear system solvers |
Applications Claiming Priority (1)
Application Number | Priority Date | Filing Date | Title |
---|---|---|---|
US12/058,494 US8068535B2 (en) | 2008-03-28 | 2008-03-28 | Robust iterative linear system solvers |
Publications (2)
Publication Number | Publication Date |
---|---|
US20090245441A1 US20090245441A1 (en) | 2009-10-01 |
US8068535B2 true US8068535B2 (en) | 2011-11-29 |
Family
ID=41114181
Family Applications (1)
Application Number | Title | Priority Date | Filing Date |
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US12/058,494 Active 2030-07-15 US8068535B2 (en) | 2008-03-28 | 2008-03-28 | Robust iterative linear system solvers |
Country Status (3)
Country | Link |
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US (1) | US8068535B2 (en) |
EP (1) | EP2269318B1 (en) |
WO (1) | WO2009120133A1 (en) |
Cited By (2)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
US20110010410A1 (en) * | 2009-07-07 | 2011-01-13 | L3 Communications Integrated Systems, L.P. | System for convergence evaluation for stationary method iterative linear solvers |
US20120098612A1 (en) * | 2009-06-26 | 2012-04-26 | Giulio Colavolpe | Reduced complexity fdm-cpm dectector with multiple access interference cancellation |
Families Citing this family (1)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
US8712738B2 (en) | 2010-04-30 | 2014-04-29 | International Business Machines Corporation | Determining ill conditioning in square linear system of equations |
Citations (10)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
US20030103212A1 (en) * | 2001-08-03 | 2003-06-05 | Volker Westphal | Real-time imaging system and method |
US20040125893A1 (en) * | 2002-12-17 | 2004-07-01 | Saeed Gazor | Methods and systems for tracking of amplitudes, phases and frequencies of a multi-component sinusoidal signal |
US20060062283A1 (en) * | 2004-09-17 | 2006-03-23 | Nokia Corporation | Iterative and turbo-based method and apparatus for equalization of spread-spectrum downlink channels |
WO2006037593A1 (en) | 2004-10-06 | 2006-04-13 | Telefonaktiebolaget L M Ericsson (Publ) | Apparatus, methods and computer program products for delay selection in a spread-spectrum receiver |
US20070280371A1 (en) * | 2004-11-04 | 2007-12-06 | France Telecom | Iterative Receiving Method For A Mimo System, And Corresponding Receiver And Computer Program |
US20080019429A1 (en) * | 1999-10-19 | 2008-01-24 | Interdigital Technology Corporation | Parallel interference cancellation method and apparatus for multiuser detection of cdma signals |
US20080090575A1 (en) * | 2006-07-13 | 2008-04-17 | Oz Barak | WiMAX ACCESS POINT NETWORK WITH BACKHAUL TECHNOLOGY |
US20090191814A1 (en) * | 2008-01-29 | 2009-07-30 | Qualcomm Incorporated | Sparse sampling of signal innovations |
US20100027590A1 (en) * | 2006-11-07 | 2010-02-04 | Girum Alebachew | Modified sir values for fast power control |
US20100303132A1 (en) * | 2009-05-27 | 2010-12-02 | Telefonaktiebolaget L M Ericsson (Publ) | Method and Apparatus for Allocating Processing Delays in Multi-Carrier Systems |
Family Cites Families (2)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
US7170924B2 (en) * | 2001-05-17 | 2007-01-30 | Qualcomm, Inc. | System and method for adjusting combiner weights using an adaptive algorithm in wireless communications system |
US7539240B2 (en) * | 2004-03-12 | 2009-05-26 | Telefonaftiebolaget Lm Ericsson (Publ) | Method and apparatus for parameter estimation in a generalized rake receiver |
-
2008
- 2008-03-28 US US12/058,494 patent/US8068535B2/en active Active
-
2009
- 2009-02-23 EP EP09726265.3A patent/EP2269318B1/en not_active Not-in-force
- 2009-02-23 WO PCT/SE2009/050196 patent/WO2009120133A1/en active Application Filing
Patent Citations (10)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
US20080019429A1 (en) * | 1999-10-19 | 2008-01-24 | Interdigital Technology Corporation | Parallel interference cancellation method and apparatus for multiuser detection of cdma signals |
US20030103212A1 (en) * | 2001-08-03 | 2003-06-05 | Volker Westphal | Real-time imaging system and method |
US20040125893A1 (en) * | 2002-12-17 | 2004-07-01 | Saeed Gazor | Methods and systems for tracking of amplitudes, phases and frequencies of a multi-component sinusoidal signal |
US20060062283A1 (en) * | 2004-09-17 | 2006-03-23 | Nokia Corporation | Iterative and turbo-based method and apparatus for equalization of spread-spectrum downlink channels |
WO2006037593A1 (en) | 2004-10-06 | 2006-04-13 | Telefonaktiebolaget L M Ericsson (Publ) | Apparatus, methods and computer program products for delay selection in a spread-spectrum receiver |
US20070280371A1 (en) * | 2004-11-04 | 2007-12-06 | France Telecom | Iterative Receiving Method For A Mimo System, And Corresponding Receiver And Computer Program |
US20080090575A1 (en) * | 2006-07-13 | 2008-04-17 | Oz Barak | WiMAX ACCESS POINT NETWORK WITH BACKHAUL TECHNOLOGY |
US20100027590A1 (en) * | 2006-11-07 | 2010-02-04 | Girum Alebachew | Modified sir values for fast power control |
US20090191814A1 (en) * | 2008-01-29 | 2009-07-30 | Qualcomm Incorporated | Sparse sampling of signal innovations |
US20100303132A1 (en) * | 2009-05-27 | 2010-12-02 | Telefonaktiebolaget L M Ericsson (Publ) | Method and Apparatus for Allocating Processing Delays in Multi-Carrier Systems |
Non-Patent Citations (1)
Title |
---|
Qing Zhao et al "Convergence behavior of iterative phase synchronization and detection," Selected Areas in Communications, IEEE Journal on , vol. 23, No. 5, pp. 932-943, May 2005. |
Cited By (4)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
US20120098612A1 (en) * | 2009-06-26 | 2012-04-26 | Giulio Colavolpe | Reduced complexity fdm-cpm dectector with multiple access interference cancellation |
US8798025B2 (en) * | 2009-06-26 | 2014-08-05 | Newtec Cy Nv | Reduced complexity FDM-CPM detector with multiple access interference cancellation |
US20110010410A1 (en) * | 2009-07-07 | 2011-01-13 | L3 Communications Integrated Systems, L.P. | System for convergence evaluation for stationary method iterative linear solvers |
US9176928B2 (en) * | 2009-07-07 | 2015-11-03 | L3 Communication Integrated Systems, L.P. | System for convergence evaluation for stationary method iterative linear solvers |
Also Published As
Publication number | Publication date |
---|---|
EP2269318A4 (en) | 2013-06-26 |
US20090245441A1 (en) | 2009-10-01 |
WO2009120133A1 (en) | 2009-10-01 |
EP2269318B1 (en) | 2015-04-08 |
EP2269318A1 (en) | 2011-01-05 |
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